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随机逼近 (SA)的目的是求未知函数f(·)的根或L(·)的极值 ,f(·)或L(·)的值可量测到 ,但量测带有噪声 .SA是处理系统控制中许多问题的重要工具 ,问题的解往往依赖于所用的SA算法的收敛性 .考察了当噪声依赖状态时SA算法的轨线收敛性 ,这里 ,状态指f(x)或L(x)的量测点x .和已有结果相比 ,加在量测噪声上的条件是最弱的 .当算法用来求f(·)的根时 ,所用条件的优点在于它可以直接验证 ,而不用顾及算法本身的行为 .当算法用来求L(·)的极值时 ,所用的条件允许量测噪声依赖状态 .加在f(·)及L(·)的条件相当一般 :求f(·)的根时 ,要求f(·)可测并局部有界 ,求L(·)的极值时 ,要求L(·)的梯度局部Lipschitz连续 .
The purpose of random approximation (SA) is to find the root of the unknown function f (·) or the extreme value of L (·), the value of f (·) or L (·) is measurable but the measurement is noisy. Is an important tool to deal with many problems in system control. The solution of the problem often depends on the convergence of the SA algorithm used. The trajectory convergence of the SA algorithm when the noise-dependent state is investigated, where the state refers to f (x) or L (x) x is the weakest condition to add to the measurement noise compared to the prior result.When the algorithm is used to find the root of f (·), the advantage of using the condition is that it can be directly Verification, regardless of the behavior of the algorithm itself.When the algorithm is used to find the extremum of L (·), the conditions used allow measurement of noise-dependent states.The conditions imposed on f (·) and L (·) are quite general: When finding the root of f (·), we require that f (·) be measurable and locally bounded, and that the local Lipschitz continuity of the gradient of L (·) be required for the extremum of L (·).